To investigate finite temperature applications, a scalar field coupled to gravity is considered. Then the Stefan-Boltzmann law and the Casimir effect are calculated. Gödel space-time is taken as the gravitational background to develop such a study. The Gödel universe, proposed by Kurt Gödel, in 1949, is an exact solution of Einstein equations that describes a rotating universe [1]}. The main feature of this metric is that it displays Closed Timelike Curves (CTCs) that allow an observer traveling along them to go back in time. As a consequence, the causality is violated. Although the Gödel universe does not present expansion, several studies with this solution have been developed [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. Here, corrections due to this space-time are calculated for the Casimir effect at zero and at finite temperature.
